Asymptotic and numerical approaches to the theory of optical microresonators and microlasers

Optical technology has an increasingly vital role in data processing and communication, with faster transmission, lower loss and larger bandwidth than comparable electronic devices, in an environment where demand for moving vast quantities of information is growing exponentially. Microlasers are micron sized dielectric resonators which trap light using total internal reflection, and can provide the intense coherent light required for this technology. For optimal performance, high 0-values, power and directionality are required. Recent experimental work has led to promising design ideas, however the current linear theory cannot explain the dependence of the lasing modes on the shape of the resonator, its index of refraction and gain, so theoretical advances are required for significant further progress. Due to the possibility of optical leakage and the existence of a non-linear gain medium in the case of active devices, such systems represent a weakly non-linear and open generalization of classical and quantum billiards widely studied in the field of quantum chaos. We propose to extend techniques commonly used in quantum chaos theory, and supplement them with powerful mathematical tools from the theory of non-linear pattern-forming systems, to address these features. In particular, this project aims to clarify the mode selection problem in microlasers, leading to design criteria for optimal performance.